Q5 of 184 Page 10

If A, B, C are the points (-1, 5), (3, 1), (5, 7) respectively and D, E, F are the middle points of BC, CA and AB respectively, prove that ΔABC = 4ΔDEF.

Given: ABC is a triangle with points (-1, 5), (3, 1), (5, 7)


To Find ABC=4DEF


We know that



Area of triangle


Then,


Area of triangle ABC




= 16


Now we have to find point D, E, and F.


Hence D is the midpoint of side BC then,


Coordinates of D



= (4, 4 )


Hence E is the midpoint of side AC then,


Coordinates of E



= (2, 6)


Hence F is the midpoint of side AB then,


Coordinates of F



= (1, 3)


Area of triangle


Now Area of triangle DEF




= 4


Therefore Area of ABC= 4 Area of DEF.


Hence Proved.


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